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Book Review: The theory of semirings \RM (with applications in mathematics and theoretical computer science\/\RM )

Hanns J. Weinert
1994 Bulletin of the American Mathematical Society  
The book can serve a reader well in many ways. The methods are explained, with lots of references given.  ...  BOOK REVIEWS 313 multidimensional problems puts severe constraints on the evolution of data and why this is a serious obstacle to finding flows which will be compatible with linear systems for which the  ...  On the other hand, since semirings and also semimodules over them have become an important tool in applied mathematics and theoretical computer science, semirings appear-sometimes with other names such  ... 
doi:10.1090/s0273-0979-1994-00476-8 fatcat:5uycwirwbvdqzacaxkc7hq4axm

Page 686 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews  
(IL-HAIF) *The theory of semirings with applications in mathematics and theoretical computer science. Pitman Monographs and Surveys in Pure and Applied Mathematics, 54.  ...  Recently, they have found extensive applications in coding theory, automata theory, the description of relational data bases, and other areas of theoretical computer science.”  ... 

Page 310 of Computational Linguistics Vol. 23, Issue 2 [page]

1997 Computational Linguistics  
The equality problem for rational series with multiplicities in the tropical semiring is undecidable. Journal of Algebra and Computation, 4. Kuich, Werner and Arto Salomaa. 1986.  ...  In J. Van Leuwen, editor, Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics. Elsevier,  ... 

Page 729 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
Since the book is primarily a textbook, it covers much less material than the reviewer’s book [The theory of semirings with applications in mathematics and theoretical computer science, Longman Sci.  ...  German summary) [Semirings] Algebraische Theorie und Anwendungen in der Informatik. [Algebraic theory and applications in computer science] Teubner Studienbiicher Mathematik.  ... 

Page 17 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
(English summary) Updated and expanded version of The theory of semirings, with applications to mathematics and theoretical computer science {Longman Sci. Tech., Harlow, 1992; MR 93b:16085].  ...  ISBN 0-7923-5786-8 This book is a carefully revised and enhanced version of The theory of semirings with applications in mathematics and theoretical com- puter science [Longman Sci.  ... 

Book Review: Automata-theoretic aspects of formal power series

Gerard Lallement
1979 Bulletin of the American Mathematical Society  
The list of references could be enriched by adding at least [1] and [2] below ([2] shows how polynomials appear in the theory of finite automata), and other applications of power-series in combinatorics  ...  mathematical approach to the theory of Kleene's regular languages, to Chomsky's context-free languages, and to various other combinatorial questions based on the idea that power-series in noncommuting  ...  and linear algebra (2) provide theoretical computer scientists with adequate and powerful tools for future research. GERARD What is mathematics?  ... 
doi:10.1090/s0273-0979-1979-14660-3 fatcat:ll2jisrwe5eopgj62e7igjjbo4

The Maslov dequantization, idempotent and tropical mathematics: a very brief introduction [article]

Grigori Litvinov
2006 arXiv   pre-print
This paper is a very brief introduction to idempotent mathematics and related topics.  ...  Since then, dozens of authors investigated matrices with coefficients belonging to an idempotent semiring and the corresponding applications to discrete mathematics, computer science, computer languages  ...  Relations to other areas and miscellaneous applications Many relations and applications of idempotent mathematics to different theoretical and applied areas of mathematical sciences are discussed above  ... 
arXiv:math/0501038v4 fatcat:xchjcg7edbebpnwhkd3ccyjkby

The design principles of a weighted finite-state transducer library

Mehryar Mohri, Fernando Pereira, Michael Riley
2000 Theoretical Computer Science  
Besides its mathematical foundation, the design also draws from important ideas in algorithm design and programming languages: dynamic programming and shortest-paths algorithms over general semirings,  ...  By taking advantage of the theory of rational power series, we were able to achieve high degrees of generality, modularity and irredundancy, while attaining competitive e ciency in demanding speech processing  ...  cases, and with the cross product of the string semiring and one of these semirings in the case of weighted transducers.  ... 
doi:10.1016/s0304-3975(99)00014-6 fatcat:fguty4gp5rca3esuvvm3ovntmm

Libor Polák (1950–2020)

Jiří Kad'ourek, Ondřej Klíma
2021 Semigroup Forum  
In the third period, he became interested in applications of algebra in theoretical computer science.  ...  Epilogue Throughout his academic life Libor Polák worked on diverse topics within algebraic semigroup theory and theoretical computer science.  ... 
doi:10.1007/s00233-021-10177-y fatcat:yqcyupmnmrcmrkl2q7npbptlmm

A Brief History of Algebra with a Focus on the Distributive Law and Semiring Theory [article]

Peyman Nasehpour
2018 arXiv   pre-print
In this note, we investigate the history of algebra briefly. We particularly focus on the history of rings, semirings, and the distributive law.  ...  Acknowledgements The author's main interests in algebra are in commutative algebra and semiring theory.  ...  The author is supported in part by the Department of Engineering Science at Golpayegan University of Technology and his special thanks go to the Department for providing all the necessary facilities available  ... 
arXiv:1807.11704v1 fatcat:wgkj42fbkvdfvepqa6tcwkiwmm

In Memoriam Zoltán Ésik

Zoltán Fülöp
2017 Acta Cybernetica  
In Szeged he was the first to teach category theory, theory of computability and complexity, logic in computer science, connections of automata and logics, fixed point theory and its applications to students  ...  In the second half of his career he worked together and obtained important results with Werner Kuich in the theory of semirings and weighted automata.  ... 
doi:10.14232/actacyb.23.1.2017.2 fatcat:wthnfyyvcbeonemfuc6y34fg4m

Page 7711 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Also an extensive bibliography (490 titles) is included to show the wide range of applications of the developed concepts in many areas of mathe- matics, computer science, physics, etc.  ...  (IL-HAIF; Haifa) * Semirings and affine equations over them: theory and applications. Mathematics and its Applications, 556. Kluwer Academic Publishers Group, Dordrecht, 2003. xiv+241 pp. $96.00.  ... 

Page 5646 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
One is based 68 COMPUTER SCIENCE 5646 on graphs and the other is based on algebraic constructions on semigroups.  ...  (English summary) Weighted automata: theory and applications (Dresden, 2002). J. Autom. Lang. Comb. 8 (2003), no. 2, 187-218.  ... 

Page 7770 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
Termination guarantees that the computation will not proceed in- definitely, and confluence guarantees that the computational result is unique even in the presence of indeterminacy.”  ...  (English summary) Theory of rewriting systems and its applications (Japanese) (Kyoto, 1995). Sirikaisekikenkyiisho Kokyiroku No.918 (1995), 1-15.  ... 


Christian Choffrut, Yoshiko Wakabayashi
2005 RAIRO - Theoretical Informatics and Applications  
Imre's vision of Computer Science Imre sees theory and practice in Computer Science as completely intertwined.  ...  of São Paulo and in 1981 a full member of the Brazilian Academy of Sciences in the area of Mathematical Sciences  ... 
doi:10.1051/ita:2005020 fatcat:anzcoji32ngorhbm52lgthpoqy
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